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Cconst

Cconst-equiv

Basic equivalence relation for cconst structures.

Definitions and Theorems

Function: cconst-equiv$inline

(defun cconst-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (cconstp acl2::x)
                              (cconstp acl2::y))))
  (equal (cconst-fix acl2::x)
         (cconst-fix acl2::y)))

Theorem: cconst-equiv-is-an-equivalence

(defthm cconst-equiv-is-an-equivalence
  (and (booleanp (cconst-equiv x y))
       (cconst-equiv x x)
       (implies (cconst-equiv x y)
                (cconst-equiv y x))
       (implies (and (cconst-equiv x y)
                     (cconst-equiv y z))
                (cconst-equiv x z)))
  :rule-classes (:equivalence))

Theorem: cconst-equiv-implies-equal-cconst-fix-1

(defthm cconst-equiv-implies-equal-cconst-fix-1
  (implies (cconst-equiv acl2::x x-equiv)
           (equal (cconst-fix acl2::x)
                  (cconst-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: cconst-fix-under-cconst-equiv

(defthm cconst-fix-under-cconst-equiv
  (cconst-equiv (cconst-fix acl2::x)
                acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-cconst-fix-1-forward-to-cconst-equiv

(defthm equal-of-cconst-fix-1-forward-to-cconst-equiv
  (implies (equal (cconst-fix acl2::x) acl2::y)
           (cconst-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-cconst-fix-2-forward-to-cconst-equiv

(defthm equal-of-cconst-fix-2-forward-to-cconst-equiv
  (implies (equal acl2::x (cconst-fix acl2::y))
           (cconst-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: cconst-equiv-of-cconst-fix-1-forward

(defthm cconst-equiv-of-cconst-fix-1-forward
  (implies (cconst-equiv (cconst-fix acl2::x)
                         acl2::y)
           (cconst-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: cconst-equiv-of-cconst-fix-2-forward

(defthm cconst-equiv-of-cconst-fix-2-forward
  (implies (cconst-equiv acl2::x (cconst-fix acl2::y))
           (cconst-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)